TI Explorer

Quick Links

Usage

You will need to have the Java runtime environment (JRE) installed on your computer in
order to use this software. As of Java Version 7 Update 51, you will also need to add
https://www.crewes.org to the Java Exception Site List. This has been tested in Windows 10
using Microsoft Internet Explorer, Microsoft Edge and Mozilla Firefox.

This Explorer can display reflection coefficients for an interface between two VTI media or between
two HTI media. Either or both of the layers may be specified as isotropic as well.
Both exact and linearized reflection coefficients may be displayed.

Version History

This explorer was first placed on the Internet on November 26, 2007.

Technical Notes

Conventional Thomsen coefficients, γ, δ, and ε, are used to define the anisotropy.
Thus the P-wave and S-wave velocities
supplied as input refer to the vertical velocities in the VTI case and to the horizontal velocities
along the symmetry axis in the HTI case.
Velocities in other directions are then derived from these using the Thomsen coefficients.
Note that Ruger and Tsvankin (1997) have also defined parameters such as δ(V) and
ε(V) which can be related to the Thomsen coefficients and which can be used in
connection with HTI. They are not used in the present version of this Explorer, but may be
incorporated as options in future versions.

The plot shows how the reflection coefficients change
with polar angle of incidence. To see how the coefficients change with polar angle of
incidence or with the elastic properties of
each medium, use features in the control panel to change these parameters.
These may be fixed to particular values in the text fields, or interactively scanned
over a range of values using the slider bars.
Drop down menus allow you to explore other useful combinations of these variables as well,
such as differences and ratios. Note that you are not prevented from selecting unphysical values of parameters.

The results are plotted in modified polar form. The
magnitude is shown as positive or negative in order that the phase will always
be zero below the first critical angle, and as continuous as possible beyond
that. (The phase below the first critical angle is not plotted in this routine.
It is always zero or pi in this region for standard polar form [when
magnitudes are always positive].) Either magnitude or phase may be deselected
for plotting using checkboxes at the bottom of the control panel.
The first quantity is plotted with a solid line and the
second with a dashed line.

Any of the scales may be adjusted using the control
panel. Angles may only be adjusted to integer numbers of degrees, and the
incident angles must be between 0° and 90°.

The locations of critical angles are indicated by
vertical lines, which are annotated with the value of the critical angle, and
the relevant velocity conditions.

The current implementation of the exact HTI solution suffers from two shortcomings.
One is that values past the critical angle are not currently calculated.
The other is that it experiences numerical instability near angles of 0° and 90°.
Fixing these defects will be an objective of future versions.